Field of the Invention
The invention relates to a method for controlling the torque of a squirrel-cage rotor asynchronous machine supplied by an inverter driven by pulse-width modulation, and can be used both generally in industrial drives and, in particular, in electric rail-bound vehicles.
The aim of virtually all drive control systems is to correct the actual torque value M of the induction machine as quickly as possible to its desired torque value M.sub.des. The torque per pole pair p of the induction machine can be calculated, for example, from the absolute values of the space vector of the total flux .vertline..sub.u .vertline. and the rotor flux .vertline..sub.r .vertline. as well as from the flux angle .theta. enclosed by the space vectors in accordance with ##EQU3## (also see the publication etz Archiv Vol. 11 (1989), Issue 1, pages 11 to 16), wherein:
.sub.u =total flux space vector; PA1 .sub.r =rotor flux space vector; and PA1 L.sigma.=leakage inductance. PA1 .function..sub.T =switching frequency of the power semiconductors; PA1 T.sub..sigma. =rotor leakage time constant; PA1 T.sub.s =stator period; and PA1 R.sub.r =rotor resistance. PA1 converting a desired torque value (M.sub.des) and an actual torque value (M) in accordance with ##EQU6## into a corresponding desired value (.omega..sub.rdes) of a rotor angular frequency and a rotor angular frequency (.omega..sub.r); and PA1 controlling the torque through a rotor frequency controller and a controller of an absolute value of a total flux in accordance with ##EQU7## wherein R.sub.r =rotor resistance; PA1 E.sub.do =rated intermediate circuit direct voltage. PA1 e.sub.0 =rated stator voltage; and PA1 a.sub..fwdarw. =steady-state space vector of the inverter drive level PA1 L.sub..sigma. =leakage inductance; and PA1 .vertline..sub.s .vertline..sub.Max =given limit of the absolute value of the stator current space vector.
The space vector magnitudes used below can be calculated according to known rules from the corresponding three phase quantities (also see IEEE Transactions on Power Electronics, Vol. 3, No. 4, October 1988, pages 420 to 429). There are no practically useful measuring transducers for flux linkages, and therefore they are generally calculated from measurable quantities by means of a machine model. In steady-state operation, the rotor flux space vector moves at a virtually constant angular velocity on a circular path.
The desired torque, which is as free as possible from distortion, is reached, for example, when the total flux space vector is likewise guided at a constant angular velocity on a circular path and defines the flux angle .theta. with the rotor flux space vector. That is virtually ideally realizable assuming quickly switching power semiconductors, because the pulse period ##EQU4## of the supply inverter is then small by comparison with the rotor leakage time constant of the machine and is also small by comparison with the stator period in the entire speed range. It holds in equation (2) that
This permits to a good approximation the simplifying assumption that the system scanned at the pulse frequency behaves in a quasi-continuous fashion and that differentials pass over into differences in accordance with EQU d/dt&lt;=&gt;.DELTA./Tp (3)
It is therefore possible in the further derivations to initially assume continuous time variations for all quantities.
The rotor flux of a squirrel-cage rotor asynchronous machine can only change slowly, with the result that rapid changes in torque can be achieved in principle only by varying the absolute value of the total flux or by varying the flux angle between the total flux and the rotor flux.
In order to already make optimum use of the power section of the drive in steady-state operation, the induction machine must always generate the required torque, which is as large as possible, by means of the minimum stator current in conjunction with the maximum absolute value of the stator voltage, that is to say in accordance with the maximum possible absolute value of the total flux. However, the maximum absolute value of the total flux must be limited to the rated flux .psi..sub.o with regard to the saturation of the stator iron.
All that thus remains is the possibility of adjusting the torque dynamically through the flux angle. The stator angular frequency .omega..sub.S, at which the electric quantities in the stator windings of the induction machine oscillate, corresponds in steady-state operation to the sum of the electrically effective angular velocity .omega. of the rotor with respect to the stator and the rotor angular frequency .omega..sub.r (rotor frequency, for short), at which the electric quantities in the rotor oscillate. For the purpose of dynamic torque adjustment, the stator angular frequency of the three-phase voltage system fed into the stator windings (stator frequency, for short) must additionally contain a dynamic component .theta. which is proportional to the rate of change of the flux angle .theta.. The stator frequency is obtained in accordance with the equation EQU .omega..sub.S =.omega.+.omega..sub.r +.theta.=.omega..sub.S +.theta.(4)
wherein .omega..sub.S =steady-state stator frequency.
The electrically effective angular velocity .omega. of the rotor with respect to the stator (designated below as the electric speed, for short) is given by the product of the pole pair number p and the mechanical angular velocity (angular frequency) .OMEGA. of the rotor in accordance with EQU .omega.=p..OMEGA. (5)
If the rotor resistance and the square of the absolute value .vertline..sub.r .vertline..sup.2 of the rotor flux, which is easy to calculate, are known, the rotor frequency is determined uniquely by the torque in accordance with ##EQU5##
The aim of all known torque controls for induction machines is to set the stator frequency specified in equation (4) in such a way that the torque follows its desired value with as good dynamics as possible, and the desired and actual torques correspond in the steady-state case.
Three-phase drives fed by pulsed inverters are increasingly being used to achieve that object. They are often fitted with so-called "field-oriented control". However, that control concept has the following disadvantages:
1. Implementing the control in a coordinate system oriented along the rotor flux space vector requires two very complicated coordinate transformations, since measured quantities that are required are always present in fixed coordinates. The desired phase voltages for the pulse-width modulation (PWM) driving the supply pulsed inverter must likewise be present in fixed coordinates. In order to provide for the coordinate transformation into the selected reference system being fixed with respect to the rotor flux, the angle .epsilon. of rotor rotation, which is determined as a rule as the integral of the speed of the rotor with respect to the stator, must be very precisely determined in common with the angular position .epsilon..sub.r of the rotor flux space vector .psi..sub.r relative to the rotor .epsilon..sub.r =.intg..omega..sub.r dt. In that case integration errors easily lead to unstable behavior, particularly given a high speed. Furthermore, it is necessary for the trigonometric functions of sin and cos to be calculated sufficiently accurately from the transformation angle, and as a rule that requires a comprehensive sin/cos table to be filed in the data memory.
2. Good torque dynamics is achieved only given adequate control reserve for the stator voltage amplitude, that is to say the stator voltage amplitude cannot already be at a maximum in steady-state operation. The steady-state use of the drive is therefore not optimum.
3. The setting of the absolute value of the total flux as a function of the working point, which is necessary in principle in field-weakening operation because of the technically limited stator voltage amplitude, is carried out in a controlled fashion, with the control laws being based on complicated calculations. They are therefore not present as a rule in closed form, and can be implemented approximately on microcontrollers only in a very complicated fashion, for example by the characteristic curves.
4. There is so far no known strategy in coordinates being fixed with respect to the rotor flux for dynamic torque adjustment without control reserve of the stator voltage amplitude, with the result that no satisfactory torque dynamics is achieved, in particular in the field-weakening range.
Due to the representation in fixed coordinates, to be sure the method presented in the publication etz Archiv Vol. 11 (1989), Issue 1, pages 11 to 16 does circumvent the transformations into coordinates being fixed with respect to the rotor flux, which are named above under number 1 as a disadvantage.
However, the following disadvantages remain: The setting of the absolute value of the total flux, which is listed above under number 3, is carried out in the field-weakening range by a PI controller. Although the calculation of the control characteristic curves is thereby eliminated, good torque dynamics is only achieved in the case of that method as well with a large control reserve of the stator voltage amplitude.
It is furthermore disadvantageous that the transient response of the control is decisively determined by the integral component of the torque controller. That is unavoidable in the case of the strategy selected there, since the integral component of the torque controller in steady-state operation must always correspond to the steady-state stator frequency .omega..sub.s in accordance with equation (4). It assumes large values in the case of a high speed, with the result that the integral component cannot be limited. Undesired transient phenomena therefore occur in the case of dynamic changes in the operating point.
Furthermore, the voltage drop across the stator resistance R.sub.s is not explicitly taken into account, with the result that it must likewise be implicitly contained in the integral components of the torque controller and the controller of the absolute value of the total flux.